President Barack Obama speaks on stage as he accepts the nomination for president during the final day of the Democratic National Convention. (Alex Wong/Getty Images)

CHARLOTTE, N.C. -- President Barack Obama concedes it will take "more than a few years" to solve the challenges "that have built up over decades."

Obama, speaking at the Democratic National Convention, said voters have a choice "between a strategy that reverses progress or one that builds on it."

Obama and Vice-President Joe Biden accepted their party's nomination for second terms.

More time needed to fix economy

As his Republican rivals campaign on the view that Americans are worse off than they were four years ago, President Barack Obama is conceding that there's been only halting progress toward fixing the nation's economic troubles.

And as he asked for a second term, the president acknowledged what he called "my own failings."

When it comes to fixing the economy, Mr. Obama said "it will take more than a few years for us to solve challenges that have built up over the decades."

But, in an appeal to independent voters who might be considering a vote for Romney, he added that "not every problem can be remedied with another government program."

The president drew cheers from delegates when he retraced his steps to halt the economic slide -- including the auto industry bailout that Mitt Romney opposed. He ridiculed his opponent's economic policies, saying that Romney believes any economic problem can be solved with a tax cut.

He told delegates, "Our path is harder -- but it leads to a better place."

Biden praises Obama's leadership traits

Vice President Joe Biden said President Barack Obama saved the country from economic collapse and deserves another term in the White House.

Biden said that he and the president are "on a mission to move this nation forward, from doubt and downturn to promise and prosperity."

Biden, who represented Delaware in the U.S. Senate, said that Mr. Obama distinguished himself in his calm and deliberative handling of the near financial collapse and deep recession not long after he took office.

He told fellow Democrats that, quote, "day after day, night after night, I sat beside him as he made one gutsy decision after another."